Aculture of yeast grows at a rate proportional to its size. if the initial population is 1000 cells and it doubles after 4 hours, answer the following questions.1)write an expression for the number of yeast cells after tt hours. p(t)=2) find the number of yeast cells after 10 hours? 3) find the rate at which the population of yeast cells is increasing at 1010 hours. answer (in cells per hour): ? ?

a)

b)

c)

Step-by-step explanation:

Part 1

For this case we assume an exponential growth model given by the following differential equation:

Where P represent the population and t the times in hours. And each 4 hours the population is doubled.

If we solve the differential equation we got:

Integrating both sides we got:

If we use exponential on both sides we got:

And for this case and we have this:

Then after 4 hours we have that the population is doubled so then would be 2000 cells and we got:

And we can solve for k like this:

So then our model is given by:

Part 2

For this case we just need to replace t= 10 hours into the model and we got:

Part 3

For this case we can find the rate like this: